You can destroy planets from the Govern planet menu (awesome option btw) But If you Destroy your starting planet, in some conditions, it crashes the game.
I started a brand new game and tried it and it didn't crash but my current game it does, it was started with the 6.1 patch so it doesn't have anything to do with old save files. I have a suspicion it has to do with the malevolent ideology tree but im not sure.
-In My game, if you set your capitol city to a different planet and then destroy the starting home planet it crashes it.
-If you set a different planet to a capital city and destroy that same planet its fine. it destroys it and then sets your starting planet back to the capital
Im not sure if its just to do with the Ruthless Trait that doubles the military production of the home world, as it doesn't work if you change your capital to a different planet.Tho it dose specifically state Homeworld Not capital so maybe that's fine. And im not sure whats happening with the Relentless trait, or if its other factors, but despite it saying +10 to homeworld and not capital, it seems to apply to what you put as your capital. So despite similar descriptions between the two they both act differently.
lastly, I might just be missing some maths in the background, but im getting some really confusing results on my planet and shipyard with both Planet Manufacturing and Military Manufacturing by changing the capital home planet around in the same turn. I dont have enough understanding about how its calculated to know for certain so i might just be mistaken.
Im guessing you might need my save? If you do where do i upload it to?